Short time existence for irregular networks was established in the paper of Ilmanen, Neves and Schulze [1]}.
They prove that if \(\Gamma _0=\lbrace \gamma _0^{(j)}\rbrace \)  is an irregular initial network, then there exists a time \(T>0\) 
and a solution of the flow \(\Gamma (t)=\lbrace \gamma _t^{(j)}\rbrace _{t\in [0,T)}\)  such that
\(\Gamma (t)\)  converges to \(\Gamma _0\)  in the sense of varifolds. (As we explain later, \(\Gamma (t)\) 
may have a larger number of arcs than \(\Gamma _0\)  itself.) Although this convergence is already slightly
stronger than requiring that \(\mathcal {H}^1\mathop {\hbox{\vrule height 7pt width .5pt depth 0pt\vrule height .5pt width 6pt depth 0pt}}\nolimits \Gamma _t \rightarrow \mathcal {H}^1\mathop {\hbox{\vrule height 7pt width .5pt depth 0pt\vrule height .5pt width 6pt depth 0pt}}\nolimits \Gamma _0\)  as \(t \rightarrow 0\) 
in the sense of measures, it is desirable to have an even more detailed understanding of the geometry
of this `singularity resolution'.
